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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

Example 1

A particle moving along the x-axis is at position x = 6 when t = 0. If

where is the particle when t = 5?

Example 2

A cat climbing up and down a tree ends at height 3 feet after 10 seconds. If  feet, how high in the tree was the cat at time t = 0?

Example 3

Let s(b) = 10.

(a) If , that means we had to take 3 away from s(a) in order to get to s(b).

(b) If , that means we had to add 7 to s(a) in order to get to s(b).

Example 4

A bicyclist is 10 miles from home after 3 hours of riding and 30 miles from home after 5 hours of riding. If her velocity is given by the function v(t), what is ?

Example 5

If s(0) = 3 and , what is s(6)?

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